$\displaystyle Z=4x^2+9y^2$
$\displaystyle y^2=-\frac{4}{9}x^2$
How to draw a graph ?
Sqare root turns out to be negative.
This one is a parabolid which opens up on the z-axis.
The problem is like you said.$\displaystyle y^2=-\frac{4}{9}x^2$
If x>0 or x<0 then we have a problem because the RHS is negative. Thus, x=0, in that case y=0 too. But there is no restriction on z, thus we move along the z-axis, thus we have a line, in fact, the z-axis.